If she lends her car to Bill, and Bill gets pulled over, and the police find contraband that is hers in the trunk...
The rights are whoever’s “effects” were in the car. I suppose by loaning the car you you could argue she delegated to him the authority to allow a search, but that didn’t happen. Nobody authorized the police to search the vehicle. It’s like the cops saying they have a right to search your apartment because you are gone and have a roommate who’s not on the lease.